Paramedic with a large urban fire department
Almost none.
If you wear a shirt that says "X Fire Department" in big letters on the back to go grocery shopping, people will come up to you and constantly ask you questions about the job. On my days off, I want to be able to fly under the radar and mentally rest for the next tour.
There are a large group of people in my field though that can't go 5 minutes without mentioning what they do to someone, have stickers are over the back of their car, and strictly wear first responder shirts to all of their functions. These people are generally frowned upon by the rest of the public safety community, but they exist and are a very vocal minority.
Meaningful? I guess. Not every call is a dramatic rescue from the clutches of death and probably didn't require a 911 call to begin with. System abuse is rampant, but there are plenty of calls where you have a few seconds to intervene or someone dies.
Important? No more or less important than a janitor or CEO. All work is necessary and helps make the world go 'round. Otherwise, it wouldn't have been made into a job opening.
Means to an end? For sure. Although I'm going to have to make a career change soon, as first responder benefits aren't what they used to be and the defined benefit pension is dead. In my days of ignorant youth, I thought getting into this field would mean helping make the world a better place. But you learn real quick that this is just a job.